Benoit moved Jeter into scoring position with a wild pitch, but struck out Bobby Abreu for the first out. He induced a groundout from Alex Rodriguez, putting Jeter on third, then intentionally walked Jason Giambi in order to challenge Matsui.
The Yankees' Japanese star was batting only .216 as he dug in, but he hammered a double to right-center for the game-winning RBI.
"It was sheer numbers," Rangers manager Ron Washington said of the choice to pit Benoit against Matsui rather than Giambi. "Jason was 2-for 10-with a bomb [lifetime against Benoit] and Matsui was 1-for-7 with six strikeouts. Plus, Jason had already gotten us earlier in the game [hitting a two-out homer in the fourth], and I wasn't going to let him do it again."
Washington's numbers on the two matchups were mostly correct, but Benoit had never struck out Matsui and didn't this time, either. The run-scoring hit sent the Rangers (10-17) to their fourth consecutive loss.
"I thought Ben could get him," Washington said, "but he didn't."
Kyle Farnsworth and closer Mariano Rivera made the lead stand up by combining on two scoreless innings of relief.
Right-hander Mike Wood turned in a solid performance for Texas when pressed into emergency service in place of Kevin Millwood. Wood made his first big-league start since last July 2 and gave the Rangers 6 1/3 competitive innings, saving the bullpen for Game 2 by allowing just three runs (two earned) on five hits.
The Yankees drew first blood with an unearned run in the second. Wood hit leadoff man Rodriguez on the arm, and the former Rangers star scampered to third base on Giambi's infield single and a throwing error by second baseman Ian Kinsler. Matsui chopped an easy double-play ball to Kinsler, but the infielder bobbled it and got only a forceout as Rodriguez scored.
Yankees left-hander Andy Pettitte squandered the lead quickly. Kinsler led off the bottom of the second with a double to left, moved to third on a Victor Diaz groundout, and scored the tying run on Gerald Laird's one-out double to right. But the chance for a bigger inning was missed when Laird got doubled off second on Michael Young's lineout to short.
"That was a mental mistake on our part on the base paths," Washington grumbled. "The ball was hit and he took off. With one out, when that ball is hit, you freeze until it goes through. You just can't get doubled off in that situation."
Giambi put the Yankees up 2-1 in the fourth, slamming a 3-1 pitch from Wood into the right-field seats for his fifth home run of the season.
New York opened a 3-1 lead in the fifth. Melky Cabrera was credited with a one-out triple on a ball that appeared to be misplayed by center fielder Jerry Hairston Jr. Cabrera scored easily on a sacrifice fly by Johnny Damon.
But the Rangers clawed back again. Teixeira opened a two-out rally in the bottom of the fifth with a single to center, and took second on a passed ball charged against Yankees catcher Jorge Posada. Sammy Sosa brought him home by driving a full-count fastball from Pettitte into the alley in right-center field. The run-scoring double gave Sosa his 21st RBI in his 24th game.
Pettitte tired after six innings and 107 pitches, and gave way to reliever Luis Vizcaino to start the seventh. Vizcaino (2-1) blew Pettitte's potential victory by giving up Hairston's first home run of the season, a 368-foot shot to left with one out in the seventh that tied the game, 3-3.
Millwood was scratched Thursday morning from his scheduled start because of a tender left hamstring.
He apparently injured his leg while taking batting practice Wednesday in anticipation of Interleague Play later this month. Millwood said the strain was moderate in nature, and that he expects to return to the rotation sometime during the team's series in New York next Tuesday through Thursday.